Subitizing is the immediate apprehension of the exact number of items in small sets. Despite more than a 100 years of research around this phenomenon, its nature and origin are still unknown. One view posits that it reflects a number estimation process common for small and large sets, which precision decreases as the number of items increases,…

In the first part of the paper, using a direct calculation two-dimensional motion of a particle sliding on an inclined plane is investigated for general values of friction coefficient ([mu]). A parametric equation for the trajectory of the particle is also obtained. In the second part of the paper, the motion of a sphere on the inclined plane is…

Deaf students often lag behind hearing peers in numerical and mathematical abilities. Studies of hearing children with mathematical difficulties highlight the importance of estimation skills as the foundation for formal mathematical abilities, but research with adults is limited. Deaf and hearing college students were assessed on the…

Standardized coefficients in logistic regression analysis have the same utility as standardized coefficients in linear regression analysis. Although there has been no consensus on the best way to construct standardized logistic regression coefficients, there is now sufficient evidence to suggest a single best approach to the construction of a…

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

How effective is training frogs to jump? This is perhaps the most frequent question in biology that is subjected to statistical analysis: does a treatment make a difference? One can examine whether there is indeed a training effect, by first assuming the opposite. That is, the authors assume that training has no effect on the mean distance jumped.…

This article comes from a question asked by a student of mine: if the Sun radiates energy in the form of electromagnetic waves, could they shift the Earth from its current orbit on a suitable timescale? The answer to such a question is apparently obvious and trivial. Nevertheless, it requires an instructive reasoning and interesting estimates of…

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…

Purpose: To estimate false-positive rates for rules proposed to identify early noise-induced hearing loss (NIHL) using the presence of notches in audiograms. Method: Audiograms collected from school-age children in a national survey of health and nutrition (the Third National Health and Nutrition Examination Survey [NHANES III]; National Center…

Looking for closed forms for an integral depending on one parameter, we obtain integral identities and new integral presentations of Catalan numbers. Wallis formula appears as an important tool.

A simple and direct method for measuring the absorption of carbon dioxide by two different substances is described. Lithium hydroxide has been used for decades to remove the gas from enclosed living spaces, such as spacecraft and submarines. The ratio of the mass of carbon dioxide absorbed to the mass of lithium hydroxide used obtained from this…

In two experiments, participants judged the average numerosity between two sequentially presented dot patterns to perform an approximate arithmetic task. In Experiment 1, the response was given on a 0-20 numerical scale (categorical scaling), and in Experiment 2, the response was given by the production of a dot pattern of the desired numerosity…

Middle school students' mathematical understanding benefits from connecting mathematics to other content areas in the curriculum. This month's activity explores the issue of the scarcity of freshwater, a natural resource (activity sheets are included). This activity concentrates on the critical areas mentioned in the Common Core State…

Density functional theory (DFT) is a type of electronic structure calculation that has rapidly gained popularity. In this article, we provide a step-by-step demonstration of a DFT calculation by hand on the helium atom using Slater's X-Alpha exchange functional on a single Gaussian-type orbital to represent the atomic wave function. This DFT…

We compared 5 different statistics (i.e., G index, gamma, "d'", sensitivity, specificity) used in the social sciences and medical diagnosis literatures to assess calibration accuracy in order to examine the relationship among them and to explore whether one statistic provided a best fitting general measure of accuracy. College…